4. A superstar goalie sometimes mishandles a harmless shot and allows a goal by mistake. The occurrence of these mistakes is assumed to be a Poisson process with A = 0.02 mistake/90 minutes. One soccer game takes 90 minutes. (Atjlkelt k! You may use P(k, t) : for the probability that a Poisson process has k arrivals for the duration of t or P(T1 0) for the probability that the inter-arrival time for the Poisson process is less than t. (a) What is the probability that the goalie makes one mistake during one soccer game? (b) This goalie has a plan to play soccer games until he makes the second mistake. Assuming no overtime/shootouts and no other issues, what is the expected number of soccer games he would play in his career